title: Simple estimators of the intensity of seasonal occurrence.
abstract: BACKGROUND
  Edwards's method is a widely used approach for fitting a sine curve to a time-series of monthly frequencies. From this fitted curve, estimates of the seasonal intensity of occurrence (i.e., peak-to-low ratio of the fitted curve) can be generated.
  
  
  METHODS
  We discuss various approaches to the estimation of seasonal intensity assuming Edwards's periodic model, including maximum likelihood estimation (MLE), least squares, weighted least squares, and a new closed-form estimator based on a second-order moment statistic and non-transformed data. Through an extensive Monte Carlo simulation study, we compare the finite sample performance characteristics of the estimators discussed in this paper. Finally, all estimators and confidence interval procedures discussed are compared in a re-analysis of data on the seasonality of monocytic leukemia.
  
  
  RESULTS
  We find that Edwards's estimator is substantially biased, particularly for small numbers of events and very large or small amounts of seasonality. For the common setting of rare events and moderate seasonality, the new estimator proposed in this paper yields less finite sample bias and better mean squared error than either the MLE or weighted least squares. For large studies and strong seasonality, MLE or weighted least squares appears to be the optimal analytic method among those considered.
  
  
  CONCLUSIONS
  Edwards's estimator of the seasonal relative risk can exhibit substantial finite sample bias. The alternative estimators considered in this paper should be preferred.
authors.affiliation: Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital & Harvard Medical School Boston, MA, USA. mbrookhart@partners.org
authors.forename: M Alan
authors.initials: MA
authors.lastname: Brookhart
authors.forename: Kenneth J
authors.initials: KJ
authors.lastname: Rothman
mesh_terms: D016001:Confidence Intervals; D004812:Epidemiologic Methods; D006801:Humans; D016018:Least-Squares Analysis; D007948:Leukemia, Monocytic, Acute / Q000453:epidemiology; D007951:Leukemia, Myeloid / Q000453:epidemiology; D009010:Monte Carlo Method; D012621:Seasons